Manipulable puzzles are very popular for recreation and amusement. In recent years, such puzzles have become increasingly challenging, spurred by the popularity and development of manipulable puzzles such as the Rubik's Cube.RTM.. Such devices are self-contained, challenging, and permit discontinuous activity without disrupting the progress toward the puzzle's solution. Furthermore, such puzzles promote hand-eye coordination as well as analytical thinking since they require the user to predict the result of each particular manipulation.